An improvement and a fast DSP implementation of the bit flipping algorithms for low density parity check decoder

For low density parity check (LDPC) decoding, hard-decision algorithms are sometimes more suitable than the soft-decision ones. Particularly in the high throughput and high speed applications. However, there exists a considerable gap in performances between these two classes of algorithms in favor of soft-decision algorithms.  In order to reduce this gap, in this work we introduce two new improved versions of the hard-decision algorithms, the adaptative gradient descent bit-flipping (AGDBF) and adaptative reliability ratio weighted GDBF (ARRWGDBF).  An adaptative weighting and correction factor is introduced in each case to improve the performances of the two algorithms allowing an important gain of bit error rate. As a second contribution of this work a real time implementation of the proposed solutions on a digital signal processors (DSP) is performed in order to optimize and improve the performance of these new approchs. The results of numerical simulations and DSP implementation reveal a faster convergence with a low processing time and a reduction in consumed memory resources when compared to soft-decision algorithms. For the irregular LDPC code, our approachs achieves gains of 0.25 and 0.15 dB respectively for the AGDBF and ARRWGDBF algorithms

Noisy Gradient Descent Bit-Flip Decoding for LDPC Codes

A modified Gradient Descent Bit Flipping (GDBF) algorithm is proposed for decoding Low Density Parity Check (LDPC) codes on the binary-input additive white Gaussian noise channel. The new algorithm, called Noisy GDBF (NGDBF), introduces a random perturbation into each symbol metric at each iteration. The noise perturbation allows the algorithm to escape from undesirable local maxima, resulting in improved performance. A combination of heuristic improvements to the algorithm are proposed and evaluated. When the proposed heuristics are applied, NGDBF performs better than any previously reported GDBF variant, and comes within 0.5 dB of the belief propagation algorithm for several tested codes. Unlike other previous GDBF algorithms that provide an escape from local maxima, the proposed algorithm uses only local, fully parallelizable operations and does not require computing a global objective function or a sort over symbol metrics, making it highly efficient in comparison. The proposed NGDBF algorithm requires channel state information which must be obtained from a signal to noise ratio (SNR) estimator. Architectural details are presented for implementing the NGDBF algorithm. Complexity analysis and optimizations are also discussed.Comment: 16 pages, 22 figures, 2 table